Low-lying Rydberg States Research Articles

Continuously tunable single-photon level nonlinearity with Rydberg state wave-function engineering

Extending optical nonlinearity into the extremely weak light regime is at the heart of quantum optics, since it enables the efficient generation of photonic entanglement and implementation of photonic quantum logic gate. Here, we demonstrate the capability for continuously tunable single-photon level nonlinearity, enabled by precise control of Rydberg interaction over two orders of magnitude, through the use of microwave-assisted wave-function engineering. To characterize this nonlinearity, light storage and retrieval protocol utilizing Rydberg electromagnetically induced transparency is employed, and the quantum statistics of the retrieved photons are analyzed. As a first application, we demonstrate our protocol can speed up the preparation of single photons in low-lying Rydberg states by a factor of up to∼40. Our work holds the potential to accelerate quantum operations and to improve the circuit depth and connectivity in Rydberg systems, representing a crucial step towards scalable quantum information processing with Rydberg atoms.

N-changing population of Rydberg states by low-energy electron-Rydberg collisions.

Inelastic n-changing collisions play an important role in the evolution of Rydberg atoms into ultracold plasmas. However, for the initially intermediate n (n ∼ 40) Rydberg states, these collisions can hardly be observed due to the low electron temperature in ultracold plasmas. In this work, we designed an experimental scheme to facilitate collisions between free electrons at 1.5eV and intermediate n Rydberg atoms. Using the field ionization technique, we measured the state distributions resulting from the evolution of initially cold rubidium atoms in the 45P3/2 Rydberg state. The experimentally obtained probability of inelastic collisions excitation agrees well with the Monte Carlo simulation results. In addition, our experimental results indicate that the n-changing population induced by hot electrons is significant for lower nP Rydberg states. Our work plays a significant role in calculating the rates of electron-ion three-body recombination in ultracold plasmas.

Theoretical study on Stark effect of Rydberg atom in super low frequency electric field measurement

AbstractSuper low frequency electric field measurements are crucial in analysing electromagnetic compatibility, assessing equipment status, and other related fields. Rydberg atom‐based super low frequency electric field measurements are performed by observing the Stark shift in the spectrum of the Rydberg state. In a specific range of field strength (E < Eavoid, where Eavoid is the threshold to avoid crossing electric fields), the Rydberg atomic spectrum experiences a quadratic frequency shift in relation to the field strength, with the coefficient being determined by the atomic polarisability α. The authors establish a dynamic equation for the interaction between the external electric field and the atomic system, and present the Stark structure diagram of the Caesium Rydberg atom. The mathematical formulae for α and Eavoid in different Rydberg states are also obtained: α = A × (n*)6 + B × (n*)7 and Eavoid = C/(n*)5 + D/(n*)7, where A(B) = 2.2503 × 10−9(7.49,948 × 10−11) and C(D) = 1.68,868 × 108(2.45,991 × 109). The error of α and Eavoid compared with the experimental values does not exceed 8% and is even lower in the low Rydberg states. Accurately calculating the values of α and Eavoid is crucial in incorporating the Rydberg atom quantum coherence effect into super low frequency electric field measurements in new power systems.

Excitation dynamics in molecule resolved by internuclear distance driven by the strong laser field.

Rydberg-state excitation of stretched model molecules subjected to near-infrared intense laser fields has been investigated based on a fully quantum model (QM) proposed recently and the numerical solutions of time-dependent Schrödinger equation (TDSE). Given the good agreement between QM and TDSE, it is found that, as the molecules are stretched, the electron tends to be trapped into low-lying Rydberg-states after its ionization from the core, which can be attributed to the shift of the ionization moments corresponding to maximum excitation populations. Moreover, the n-distribution is broadened for molecules with increasing internuclear distance, which results from the change of momentum distribution of emitted electrons. Analysis indicates that both of the above phenomena are closely related to the interference effect of electronic wave packets emitted from different nuclei. Our study provides a more comprehensive understanding of the molecular excitation in intense laser fields, as well as a means of possible applications to related experimental observations.

Field emission angular distribution from single molecules

We demonstrate that the field emission from a single molecule at the apex of a metallic tip exhibits a well-defined angular distribution pattern (field emission angular distribution, FAD) with a spherical harmonics shape, regardless of the species of the molecule. From carefully controlled simultaneous measurements of the emission pattern, the emission current and emission energy, we deduced the formation mechanism of the FAD pattern in which the electron from the metallic tip resonantly tunnels into vacuum via a molecule-induced state situated at the Fermi level of the tip. The characteristic FAD patterns were consistent with the Fourier transform of the superatom molecular orbitals (SAMOs). Thus, the present method is unique for real-time imaging of the SAMOs, or the low-lying Rydberg states, of single molecules.

Cover Feature: Norbornadiene/Quadricyclane System in the Spotlight: The Role of Rydberg States and Dynamic Electronic Correlation in a Solar‐Thermal Building Block (ChemPhotoChem 4/2023)

The Cover Feature illustrates the photophysics and photochemistry of the norbornadiene (NBD) and quadricyclane (QC) molecular switch pair by the characterization of the low-lying valence and Rydberg states by means of CASPT2//CASSCF multireference theory. Two low energy conical intersections were identified for both the NBD↔QC photochemical reaction revealing that the photorelaxation is ruled by the deformation of two coupled reaction coordinates and the nonadiabatic population exchange is facilitated by a doubly excited valence state. More information can be found in the Research Article by Marco Marazzi, Mariachiara Pastore and co-workers.

The fine and hyperfine structures of the low-n 3Π u Rydberg states of H2 revisited

The experimental fine and hyperfine structures of low Rydberg states with 2–4 measured in the 1970's for various vibration-rotation levels by Lichten and collaborators, and by Miller and Freund, are reanalysed in the framework of molecular frame-transformation multichannel quantum defect theory MQDT. Instead of the level by level treatment in terms of an effective Hamiltonian as was carried out at the time, a global theory is applied to all levels at once. It is found that the essence of the observed level patterns is well represented by MQDT in terms of a substantially reduced number of dynamical parameters – quantum defects – although the experimental accuracy of the experiments is not yet quite reached. Possible reasons for the remaining discrepancies are given. Since quantum defect theory MQDT, a formalism derived from scattering theory, is still rather little used in the domain of modern ultra-high precision spectroscopy, the occasion is taken here to review some of its key elements.

The excited states of azulene: A study of the vibrational energy levels for the lower ππ*-valence states by configuration interaction and density functional calculations, and theoretical studies of the Rydberg states.

A new vacuum ultraviolet absorption (VUV) spectrum of azulene vapor has been obtained by using a synchrotron radiation source. The onset of the ultraviolet spectrum, previously reported by Sidman et al., has been analyzed in detail by Franck-Condon (FC) and Herzberg-Teller (HT) methods. The photoelectron spectral profile identifies the 3px-Rydberg state 00 band to be 131cm-1 from the VUV maximum. Excited state energy levels were calculated by three independent methods: the wide scan VUV spectrum was correlated with symmetry adapted cluster configuration interaction calculations. The low energy portion of the spectrum was studied by both time dependent density functional theoretical methods (TDDFT) and multi-reference multi-root CI (MRD-CI). Equilibrium structures were determined for valence states at the TDDFT level. Rydberg states were determined by both TDDFT and MRD-CI. The FC + HT analyses were performed on the TDDFT wave-functions. The HT intensity profiles are generally low in intensity, relative to the FC ones; however, HT is dominant in the second singlet state (S2, 11A1). As a result, numerous non-symmetric modes, their overtones, and combination bands show considerable intensity in that band. Energies obtained from use of extremely diffuse s-, p-, d-, or f-character functions enabled realistic extrapolation to the IE1 for many Rydberg states (RS). The lowest RS (3b13s) based on IE2 lies at 4.804eV with a quantum defect of 0.714. Differentiation between valence and RS is readily made using the second moments of the charge distribution.

Predissociation Dynamics of Br2 in the [2Π1/2]c5d; 0g + and [2Π3/2]c6d; 0g + Rydberg States by Velocity Map Imaging Study.

We investigated the predissociation dynamics from the [2Π1/2]c5d; 0g+ and [2Π3/2]c6d; 0g+ Rydberg states of Br2 using the velocity map imaging technique. Two-dimensional scattering images of the fragmented Br+ exhibited an isotropic feature upon the excitation of these Rydberg states. Analysis of the total kinetic energy release suggested the existence of the predissociation pathways to the dissociation limits of Br(5s, 4P3/2) + Br(4p, 2P3/2) and Br(5s, 4P5/2) + Br(4p, 2P3/2) via the 0g+ ion-pair states that interact with the lower and/or excited-core Rydberg states lying at long internuclear distance regions thorough the avoided crossing.

Observation of the Rydberg Resonance in Surface Electrons on Superfluid Helium Confined in a 4-$$\mu$$m Deep Channel

We report the first observation of the microwave-induced intersubband (Rydberg) resonance in the surface-bound electrons on superfluid helium confined in a single 4-$\mu$m deep channel. The resonance signal from a few thousand of surface electrons comprising the Wigner Solid (WS) is detected by observing WS melting due to the microwave absorption. The observed transition frequency for the two lowest Rydberg states, in the range of 0.4-0.5 THz, is determined by the image charges induced by the surface electrons in conducting electrodes of the microchannel and the potentials due to applied voltages, and is in a good agreement with our calculations. The observed large broadening of the resonance on the order of 10 GHz, which is due to inhomegeneous distribution of the pressing electric field in the microchannel, is also in a reasonable agreement with our finite-element modeling calculations. This study of the confined electrons is motivated by their potential use for charge and spin qubits.

The corrections to quantum defect for high n Rydberg atoms

Quantum defect converges to constant value at high Rydberg series in quantum defect theory. In experiments, it is usually distorted by the shift of ionization limit, external magnetic field, or external electric filed. The shift of ionization limit has cubic power of effective quantum number correction to the quantum defect, while the magnetic and electric field has seventh and tenth power of effective quantum number correction, respectively. The simulation shows that the electric field correction to the quantum defect is very small at low Rydberg states, but it increases quickly at high Rydberg states and even exceeds the correction from the shift of ionization limit. The correction to quantum defect is up to 0.93 at n0*=80. The two scenarios can be distinguished by fitting the experimental data, and the energy spectrum can be obtained more accurately by fixing the corrections.

Controlling quantum numbers and light emission of Rydberg states via the laser pulse duration

High Harmonic Generation (HHG) creates coherent high frequency radiation via the process of strong field ionization followed by recombination. Recently, a complementary approach based on Frustrated Tunnel Ionization (FTI) was demonstrated (Nature Photonics 12, 620 (2018)). It uses spectrally separated peaks created by lower quantum number Rydberg states to produce coherent extreme ultraviolet (EUV) light. While much is understood about enhancing emission from HHG by controlling recombining electron trajectories, relatively little is known about controlling the quantum number distribution of Rydberg states. This distribution is generally believed to be determined primarily by field strength and laser frequency. We show that, in fact, it also changes significantly with the duration of the laser pulse: increasing pulse duration depletes lower-lying Rydberg states, thereby substantially decreasing EUV yield. Using electron trajectory analysis, we identify elastic recollision as the underlying cause. Our results open a door to greater control over production of coherent high frequency radiation, by combining FTI and HHG mechanisms, and also improved the interpretation of molecular imaging experiments that rely on elastic electron recollision.

Directional THz generation in hot Rb vapor excited to a Rydberg state.

We optically excite 85Rb atoms in a heated vapor cell to a low-lying Rydberg state 10D5/2 and observe directional terahertz (THz) beams at 3.3 THz and 7.8 THz. These THz fields are generated by amplified spontaneous emission from the 10D5/2 state to the 11P3/2 and 8F7/2 states, respectively. In addition, we observe ultraviolet (UV) light produced by four-wave mixing of optical pump lasers and the 3.3 THz field. We characterize the generated THz power over the detuning and power of pump lasers, and identify experimental conditions favoring THz and UV generation, respectively. Our scheme paves a new pathway towards generating high-power narrowband THz radiation.

Preparation of Long-Lived, Non-Autoionizing Circular Rydberg States of Strontium.

Alkaline earth Rydberg atoms are very promising tools for quantum technologies. Their highly excited outer electron provides them with the remarkable properties of Rydberg atoms and, notably, with a huge coupling to external fields or to other Rydberg atoms while the ionic core retains an optically active electron. However, low angular-momentum Rydberg states suffer almost immediate autoionization when the core is excited. Here, we demonstrate that strontium circular Rydberg atoms with a core excited in a 4D metastable level are impervious to autoionization over more than a few millisecond time scale. This makes it possible to trap and laser-cool Rydberg atoms. Moreover, we observe singlet to triplet transitions due to the core optical manipulations, opening the way to a microwave to optical quantum interface.

The vacuum ultraviolet spectrum of cyclohepta-1, 3, 5-triene: Analysis of the singlet and triplet excited states by ab initio and density functional methods.

The vacuum ultraviolet (VUV) spectrum for cyclohepta-1,3,5-triene up to 10.8 eV shows several broad bands, which are compared with electron impact spectra. Local curve fitting exposed groups of sharp vibrational peaks, which are assigned to Rydberg states. The vertical excitation profile of the VUV spectrum, reproduced by time dependent density functional theory (TDDFT), gives a good interpretation of the principal regions of absorption. Fourth order Möller-Plessett perturbation theory, including single, double, and quadruple excitations, showed that the lowest singlet and triplet states retain CS symmetry. This contrasts with TDDFT where several low-lying excited states are planar. Detailed vibrational analysis of the first UV band was performed by Franck-Condon, Herzberg-Teller, and their combined methods. These show the dominance of mid-range frequencies, while the lowest frequency (75 cm-1) has negligible importance. In contrast, the second excited (Rydberg) state shows a major progression with separations of 115 (6) cm-1. This is interpreted by re-analysis of the X2A' ionic state at the anharmonic level. Extremely low exponent Gaussian functions enabled several low-lying Rydberg state energies to be determined theoretically; extrapolation of the 3s-, 4s-, and 5s-Rydberg state calculated energies gives the adiabatic ionization energy as 7.837 eV (4) with δ 0.964 (2). Similarly, extrapolation of the centroids of the observed Rydberg states gave the vertical ionization energy (VIE) as VIE1 = 8.675 ± 0.077, close to the photoelectron spectroscopy VIE value [8.55 (1) eV].

Electron capture to the Rydberg atomic states in ternary collisions with neutral particles

SynopsisWe report on the results of theoretical comparative studies of different physical mechanisms of free electron capture to the Rydberg atomic states and bound-bound transitions in discharge plasmas of Ne/Xe and Ar/Xe mixtures containing atomic and molecular ions. Particular attention is paid to the role to the resonant non-adiabatic free-bound and bound-bound transitions due to collisions with neutral particles. We show that in a wide range of low-temperature plasma parameters the contribution of resonant processes to the population of low-lying Rydberg states is predominant.

Measurement of 85Rb nP-state transition frequencies via single-photon Rydberg excitation spectroscopy

We report the measurement of transition frequencies of Rb85 atoms in a room-temperature vapor cell to nP1/2 (n=34–53) and nP3/2 (n=34–87) Rydberg levels by observing single-photon Rydberg excitation spectroscopy. Based on the spectroscopic data, we determine quantum defects that are in good agreement with previous measurements of low-lying Rydberg states. Furthermore, the residuals between observed and calculated values of fine-splitting intervals in our experiments are found to be less than 10 MHz.

Collimated UV light generation by two-photon excitation to a Rydberg state in Rb vapor

We use two continuous-wave (CW) laser beams of 780 nm and 515 nm to optically drive $^{85}$Rb atoms in a heated vapor cell to a low-lying Rydberg state 10D$_{5/2}$. We observe a collimated ultraviolet (UV) beam at 311 nm, corresponding to the transition frequency from the 11P$_{3/2}$ state to the 5S$_{1/2}$ state. This indicates the presence of a coherent four-wave mixing process, built up by two input laser fields as well as a terahertz (THz) radiation of 3.28 THz that is generated by amplified spontaneous emission between the 10D$_{5/2}$ and the 11P$_{3/2}$ states. We characterize the 311 nm UV light generation and its dependence on various physical parameters. This scheme could open up a new possibility for generating narrow-band THz waves as well as deep UV radiation.

Rydberg states of the CdAr van der Waals complex

A theoretical study of the relatively unexplored area of low-lying Rydberg states of van der Waals molecules (vdW) in the particular case of the CdAr system is presented. The fully ab initio calculation of the potential energy curves (PECs) of the excited vdW complex CdAr above the $(5s6s)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}S_{1},^{\phantom{\rule{0.16em}{0ex}}1}S_{0}$ atomic asymptotes, reaching the $(5s6p)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}P_{0,1,2}, (5s5d)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}D_{2}{,}^{3}{D}_{1,2,3}, (5s6p)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}P_{1}$, and $(5s7s)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}S_{1},^{\phantom{\rule{0.16em}{0ex}}1}S_{0}$, is performed. All the calculated PECs of the Rydberg states of $\mathrm{\ensuremath{\Sigma}}$ symmetry exhibit undulations resulting in the double-well character that was already observed experimentally in the case of the lowest Rydberg states of various 12 group metal--rare gas vdW complexes. The outer wells obtained within the present work are shallow with depths not exceeding 20 ${\mathrm{cm}}^{\ensuremath{-}1}$ below the atomic asymptote and reaching equilibrium distance of roughly 27 bohr in the case of states correlating with the $(5s7s)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}S_{1},^{\phantom{\rule{0.16em}{0ex}}1}S_{0}$ asymptotes. The largest calculated values of permanent electric dipoles at equilibrium distances exceed 10 D in the case of ${}^{1}\mathrm{\ensuremath{\Sigma}}$ Rydberg states correlating with $(5s6p)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}P_{1}$ and $(5s5d)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}D_{2}$ atomic asymptotes. The calculations were performed within the second-order multireference perturbation theory. The performance of this particular theoretical ab initio approach is discussed in the context of the considered type of systems and compared, wherever it was possible, with the benchmark results of the coupled-cluster method obtained in this work, with other ab initio calculations based on multireference perturbation theory and experimental data.

Nonadiabatic Investigation of the Electronic Spectroscopy of trans-1,3-Butadiene.

Low-lying UV spectroscopy of trans-1,3-butadiene has been extensively studied by experimentalists and theorists. Though a host of techniques has been applied to understand its lowest electronic states, there are still important open questions. Among these are the positions of the two lowest valence excited states and the factors responsible for the spectral shape of the lowest allowed transitions. We present results from EOM-CC calculations in extended basis sets that are used to parametrize a three-electronic-state Koppel, Domcke, and Cederbaum (KDC) model. We test the sensitivity of the KDC model to a variety of parameters and address several outstanding questions regarding the spectrum. We find that the overall shape of the spectrum is determined primarily by the Franck-Condon envelope of the 11Bu state and that the princple impact of the doubly excited 21Ag state is to broaden the 11Bu peaks. There is only modest sensitivity to the relative position of these two states. We find that the lowest Rydberg state, the 11Bg state, has an unexpected impact on the third peak in the spectrum, and its effect is considerably more energy-dependent than that of the 21Ag state.